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Concept

Young tableau

Related publications (13)

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Pierre Marcel Nataf, Samuel Gozel

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

2020

Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains

Samuel Gozel

In this thesis we study various one-dimensional quantum spin systems with SU(2) and SU(N) symmetry. We investigate the short-distance behavior of the SU(2) Heisenberg model in the limit of large spin and show that there exists an extended regime where pert ...

EPFL2020

Self-conjugate representation SU(3) chains

Frédéric Mila, Miklos Lajko, Francisco Hyunkyu Kim

It was recently argued that SU(3) chains in the p-box symmetric irreducible representation (irrep) exhibit a "Haldane gap" when p is a multiple of 3 and are otherwise gapless [Nucl. Phys. B 924, 508 (2017)]. We extend this argument to the self-conjugate ir ...

2019

Maximal subgroups acting with two composition factors on irreducible representations of exceptional algebraic groups

Nathan Scheinmann

Let

Y

be a simply connected simple algebraic group over an algebraically closed field

k

of characteristic

p

and let

X

be a maximal closed connected simple subgroup of

Y

. Excluding some small primes in specific cases, we classify the

p

-restrict ...

EPFL2019

Density matrix renormalization group simulations of SU(N) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

Frédéric Mila, Pierre Marcel Nataf

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N) Heisenberg chain with open boundary conditions taking full advantage of the SU(N) symmetry of the problem. This method is an extension of the method pre ...

2018

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting ...

2017

Complex magnetic incommensurability and electronic charge transfer through the ferroelectric transition in multiferroic Co3TeO6

Helmuth Berger, Yang Zhao

Polarized and unpolarized neutron diffractions have been carried out to investigate the nature of the magnetic structures and transitions in monoclinic Co3TeO6. As the temperature is lowered below 26 K long range order develops, which is fully incommensura ...

Springer Nature2017

Linear flavor-wave theory for fully antisymmetric SU( N ) irreducible representations

Frédéric Mila, Pierre Marcel Nataf, Francisco Hyunkyu Kim

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU(N) is presented in order to investigate the color order of SU(N) antiferromagnetic Heisenberg models in several two-dimensional geometries. The ...

2017

Anatomical and functional properties of the foot and leg representation in areas 3b, 1 and 2 of primary somatosensory cortex in humans: A 7T fMRI study

Olaf Blanke, Andrea Serino, Wietske Van der Zwaag, Roger Gassert, Roberto Martuzzi, Michel Akselrod

Primary somatosensory cortex (S1) processes somatosensory information and is composed of multiple subregions. In particular, tactile information from the skin is encoded in three subregions, namely Brodmann areas (BAs) 3b, 1 and 2, with each area represent ...

2017

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...

EPFL2016

Exact diagonalization of HeisenbergSU(N)chains in the fully symmetric and antisymmetric representations

Frédéric Mila, Pierre Marcel Nataf

Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg SU(N) Hamiltonian with several particles per site living in a fully symme ...

2016

Exact Diagonalization of Heisenberg SU(N) Models

Frédéric Mila, Pierre Marcel Nataf

Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the ...

2014

Defect of characters of the symmetric group

Following the work of B. Kulshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the l-defect of characters of the symmetric group G(n), where l > 1 is an arbitrary integer. We prove that the l-de ...

De Gruyter2009